We report neutron-diffraction measurements of the magnetic phase diagram of the colossal magnetoelectric DyMn2O5. Our measurements reveal the magnetic origin of the complex dielectric anomalies in this material. Frustrated magnetic interactions result in a large density of low-energy magnetic states which can be selected by the application of relatively small magnetic fields. The unusual combination of magnetic frustration and strong magnetoelastic coupling is responsible for the remarkable changes of the dielectric properties of DyMn2O5 in small applied magnetic fields.
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